The analysis in [1]} after they make the Lagrange multiplier a propagating field, proceeds along the lines of the non-perturbative ERG equations. They were following [2]} where the bound states in a model with a single fermion were studied and a kinetic term for the auxiliary scalar was added to the fermion action ad hoc. In [2]} and [1]} the \({1\over N}\)  approximation used normally for studies of fermion condensates is not available.
